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Introduction

The development of the human brain is probably one of the most interesting topics in the observation of neonates and premature infants. Definition of anatomical and temporal characteristics of development of critical brain structures in the living premature infant is crucial for an insight into the time of greatest vulnerability in such structures.

Diffusion tensor magnetic resonance imaging is the only noninvasive means available today that approaches the molecular diffusion process in vivo and therefore allows the observation of the microstructural development in the human newborn cerebral white matter.

Different studies have been performed to analyze this development quantitatively [2] [6]. Other studies use this imaging modality for an early detection of small injuries [4] [5].

The inter-subject comparison of this microstructural development will make it possible to build a statistical atlas for the normally developing brain. Comparing this atlas to single subjects could allow the early detection of injuries or abnormalities. A first step to build such an atlas is the rigid and nonrigid registration of two different subjects to remove natural inter-subject differences. This work presents a method on how to match tensor images, which represent the molecular diffusion process, of different subjects.

• Chapter 2 gives an insight on the medical application for which this work was done.
• Chapter 3 explains how diffusion tensor images are acquired with magnetic resonance technologies and the characteristics of human brain in this image modality.
• Chapter 4 discusses some general characteristics of the tensor data structure, different measurements that can be applied, and finally some ways of visualizing tensor data.
• Chapter 5 to 7 present the data processing path from the scanner to the nonrigid matching of two different data sets. This path is illustrated in Figure 1.1. Chapter 5 describes the preprocessing which entails the conversion of the scanner output into tensor data, i.e. solving the equations presented in Chapter 3 as well as the generation of the corresponding tensor data structure. In Chapter 6 the process of rigidly aligning two images (and specifically tensor data) is described. Chapter 7 finally presents the nonrigid registration of two data sets and all the methods involved.
• Chapter 8 is a short presentation of some ways of segmenting diffusion tensor data. It should be mentioned that this is only a description of the segmentations that can easily be performed with the current implementation, but there is no further investigation on the quality and meaning of the segmentation.
• Chapter 9 gives an overview of the program structure, the interaction and function of the different classes and the data representation. Appendix A includes a description of the most important functions.
• Chapter 10 presents some conclusions and discusses different extensions and improvements that should be considered.

Through this report $D$ will denote a tensor which is a symmetric $3 \times 3$ matrix. Positions in an image or volume $\Omega$ of any type are indexed with $i, j, k$ for the x, y and z dimensions respectively, so that $D(i,j,k)$ refers to the tensor at position $(i,j,k)$. The dimensions of the volume are $X, Y$ and $Z$, and the voxel dimensions are $\delta_X$, $\delta_Y$ and $\delta_Z$. When comparing two data sets the index S identifies the reference or stationary image, which will not be displaced. The index M refers the moving data set which will be displaced according to a displacement field $U = (v, v, w)^T$ to better match the stationary data set.

A tensorfield denotes a field or volume of tensors which represents the data set. When decomposing the tensor into an eigenvalue, -vector, i.e. an eigensystem, the term eigenfield will be used to describe the data set.

Figure 1.1: Data processing path